Saturday, 27 September 2014

To construct the figure:
(i) Measure and draw line AB using ruler.
(ii) Measure and draw angle ABC using protractor.

(iii) Stretch the 2 arms of the compass to measure 5.2 cm and mark an arc on the line BC. Label it point C.

Here are 2 ways of drawing the parallel line DC
(iv) Use a protractor to draw angle BCDOR
(iv) Use a set-square and ruler to draw line CD
(v) Stretch the 2 arms of the compass to measure 3.8 cm, place the sharp end at "C" and mark an arc on the line DC. Label it point D.

Estimation involves calculation, whereas Approximation is about rounding off a number.

The rounding off of a number can be carried out before or after the calculation.

Consider the following scenario:

The length of the door is 1.95 m and its height is 2.06 m (assuming that the dimensions given are exact).

(a) Find the area of the door and round the answer off to 2 significant figures.

The actual area of the door is 1.95 m x 2.06 m = 4.017 m^2.

Answer = 4.0 m^2 (to 2 sig fig) [Ans]

The step to round off a number (to present the final answer) is an approximation.

There is no mention of estimation in question (a), so we use the given values to compute the area first, then round off as required.

(b) Estimate the area of the door to 2 significant figures.

The purpose of doing 'estimate' or 'estimation' is to enable us carry out calculation quickly and when we don't need an exact value. A rough figure should give us a sense of the actual value. It should not be too far off from the actual value.

To estimate, we will round the numbers off to the required "degree of accuracy" (in this case, 2 significant figures) first before doing any calculation. In other words, we are using the approximated numbers to do calculation.

Area of the door ≈ 2.0 m x 2.0 m <<<<< This is the 'estimation' step when the approximated values are used for calculation

= 4.0 m^2 [Ans]

Since 1.95 m ≈ 2.0 m (2 sig fig) and 2.06 m ≈ 2.0 (2 sig fig)

Exception

When doing Estimation, we round off the values based on the degree of accuracy given.

However, there is an exception when dealing with roots because by rounding it off to 1 SF, 2 SF, etc. may not land itself nicely to be rooted.

To estimate square root of 26.77, it does not help us to figure out what number it's 'near' to if we round it off to 1 SF (i.e. 30) or 2 SF (i.e. 27).

However, we know that 25 (which is a perfect square) is quite close to it; so, we will estimate it to be square root of 25, and get the answer "5".

If you key square root 26.77 in the calculator, your answer should be quite close to 5.

Friday, 19 September 2014

As you should have moved into the final stage of the exam preparation in Term 4 Week 2, instead of conducting remedial lessons, I've created several consultation slots so that you can see me to go areas that you are not sure, e.g. questions in the revision papers.

22 Sep (Monday) 2.30 pm to 4.30 pm

24 Sep (Wednesday) 1.45 pm to 2.15 pm

29 Sep (Monday) 11 am to 12 noon

30 Sep (Tuesday) 12 noon to 1 pm

You may give me a call (@419, outside the staff room) or send me an email alert.

Tuesday, 9 September 2014

How to find "The number of sides a regular polygon has if its exterior angle is ≥180º?

In the syllabus, we focus on convex polygons.
One of the properties that all convex polygons have would be the sum of Interior and Exterior angles is 180º.
Hence, the size of each exterior angle cannot be more than 180º.

Below are 2 examples of polygons with exterior angles being acute angle and obtuse angle.

Monday, 1 September 2014

Some of you enquired the "complete" set of solution (after the class discussion) - i.e. the various possibilities that arise from various assumptions.

Here are the possibilities and assumptions that we need to be clear before solving the problem:

In scenario 2, some of you suggested using nets (something you learnt in primary school).
Here, it's good to draw the net and write the dimensions clearly to ensure the correct numbers are used for calculation.

Look, there are 2 possible 'nets' that could give the shortest path.
Do NOT assume the 2 nets give the same "diagonal" length.
[Do not apply "seeing is believing"]
Always compute the numbers to check.

The 3rd scenario was the one that we spent a significant amount of time to discuss in class - Refer to the "Romeo & Juliet" box that I brought to the class to help you visualise better.
Here, you would have to apply Pythagoras Theorem twice.

Useful Links

Information about AssessmentsClick HERE to view the suggested Scheme of Work

Submission of Homework (Hardcopy)

Written homework is usually due by the following lesson.

If you are unable to submit the piece of work during the lesson, you should submit it to my pigeonhole, outside the staff room by the end of the day.

If you forget to bring your homework, you should take a picture of the homework and email to me by the end of the day as an evidence that you have completed the work. You should submit the work to my pigeonhole when you return to school the following day.